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A quick Google search on mathematics metacognition returns more than 300,000 results. What is metacognition and why should we care about it? The Merriam-Webster dictionary defines it as
Awareness or analysis of one’s own learning or thinking processes.
I find that often, students are not processing the information being given to them in useful ways. For instance, when learning a new mathematical concept, many students just memorize the concept. However, reflecting upon the foundation of that concept will serve them better by providing them with a framework for the material.
Perhaps this is because students are not taught to reflect upon their learning and thinking enough. If this is the case, how can we encourage students to do this self-reflection? I am using Dr. Cynthia Young’s Precalculus with Limits textbook this semester. One of the features I really like about the book is that it lists objectives at the beginning of each chapter and each section. This makes it quite easy for students to go through the list and reflect upon their understanding of the core ideas covered in each section.
I have started trying a new strategy myself (I believe it is called the Cornell style). I take all of my notes on my iPad. I asked one of my friends to create the template to the left for me. I take my notes in the space between the two blue lines and label in the margin if something is a theorem, definition, example, etc. Later, I go back and summarize what is on the page in the five lines below the bolded blue line.
What do you do to reflect on your learning and thinking? Do you have strategies for getting your students to practice metacognition in and outside of the classroom?